1. When, the formula 2x+ 14π is meaningful in the real number range.
2. Decomposition factor: 6x3-7x2+x = _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. If the equation y-8y-7- 17-y = 8 has roots, then the roots are y = _ _ _ _ _ _ _
The absolute value of 4.2-5 is _ _ _ _ _.
5. A factory used to use X tons of coal every day, but after taking coal-saving measures, it can use 3 tons less every day. If there are 30 tons of coal now, it can take a few more days than before after taking coal-saving measures.
6. If the area of a dragonfly is 24 and the length of one diagonal is 6, then the length of the other diagonal is _ _ _ _ _ _ _.
7. The quadrilateral with two diagonal lines _ _ _ _ _ _ _ _ _ _ is a rectangle.
8. It is known that in the parallelogram ABCD, AB = 3 cm, BC = 5 cm, and the bisector of BE ∠ABC intersects with AD at point E, then DE = _ _ _ _ _ _ _ _ cm.
9. As shown in the figure, if two rectangles with the same size are combined into an L-shaped pattern, then △ACF is? _ _ _ _ _ _ triangle.
10. There are four small sticks with lengths of 1cm, 2cm, 3cm and 4cm respectively. Choose three sticks at random, and the probability that three sticks can form a triangle is _ _ _ _ _ _ _ _.
Second, multiple-choice questions: (2 points for each question, 20 points * * *)
1 1. The following numbers: 0.2, -233, π2, 3343,12,227,1+5,0.10100/
A.3 B.4 C.5 D.6
12. The one-to-one correspondence with the points on the number axis is ().
A. Real number B. Irrational number C. Rational number D. Integer
13. The following operation is correct ()
A.a4+a5=a9 B.a3？ a3？ a3=3a3
C.2a4×3a5=6a9 D.(-a3)4=a7
14. The following factorization is correct ()
A.a4-9a2+8=(a2- 1)(a2-8)
B.(3 x2+5x)2+(3 x2+5x)-6 =(3 x2+5x+3)(3 x2+5x-2)
c . x4-x3-x+ 1 =(x- 1)2(x2+x+ 1)
D.a2+7a-6=(a+ 1)(a+6)
15. given XA = 3, XB = 5, X3A-2B = ()
A.2725 B.9 10 C.35 D.52
16. The library plans to buy a certain kind of book. If you buy it in 60 yuan, you will buy five more books. If they were bought in 40 yuan, they would buy five books less. If x is needed, the following equation is correct ().
A.40x+5=60x B.60x+5=40x-5
C.60x-5=40x+5 D.60x+5=40x
17. in right-angled trapezoidal ABCD, AB‖DC ∠ B = ∠ C = 90? , if AD = 20, BC = 10, AB > CD, then the sizes of ∠A and ∠D are () respectively.
.30 caliber? , 150? B.45？ , 135? C. 120？ ,60? D. 150？ ,30?
18. Which of the following features does a diamond have but a rectangle does not ()?
A. instability
B. The diagonal line is equally divided
C. the sum of internal angles is equal to the sum of external angles.
The straight line of each diagonal line is its axis of symmetry.
19. The following statement:
① Regular pentagons are axisymmetric figures;
② The regular pentagon is a rotationally symmetric figure, not a centrally symmetric figure;
③ The regular pentagon is a central symmetrical figure;
(4) The regular pentagon is an axisymmetric figure and a central symmetric figure;
⑤ Regular pentagon is an axisymmetric figure and a rotationally symmetric figure.
The correct one is ()
A.2 B.3 C.4 D.5
20. If you roll two orderly dice, your chances of getting two "2" s will be ().
a . 16 b . 13 c . 1 12d . 136
Third, answer questions:
2 1. Calculation: (4 points for each question, 16 points * * *)
① 3(- 1)2+3-8+3-| 1-3 |
② a―(a2b―2a3b2)÷ab
③(x2+3)2-2(x+3)(x-3)(x2+9)+(x2-3)2
④ (xy-x2)÷x2-2xy+y2xy？ x-yx2
22. Factorization: (4 points for each question, * * * 8 points)
① (x2+y2)2-(2xy)2
② factorization: 2 (3a2-b)-a (3b-4)
23. Solving equations: (4 points for each question, * * * 8 points)
① 5x―42x―4=2x+53x―6― 12
② xa2-a=xb2-b (a≠ b)
24. It is known that in parallelogram ABCD, m is the midpoint of AD, and MB = mc.
Verification: The quadrilateral ABCD is a rectangle. (4 points)
25. Simplified evaluation: xx-y? Y2x+y-x4yx4-y4 ÷ x2x2+y2。 Where x = 2, | y- 1 | = 1. (4 points)
26. if a = a+b-3a+7 is the arithmetic square root of a+7 and b = 2a-b+22b+2 is the cubic root of 2b+2,
Find the square root of A-B (4 points)
27. Given A2-4A+ 1 = 0, find the value of the algebraic formula A2A4+A2+ 1. (4 points)
During the holiday, the workers went to a scenic spot 25 kilometers away from the factory. Some people ride bicycles. 1 hour after 20 minutes, the rest of you will leave by car. As a result, two people arrived at their destination at the same time. As we all know, the speed of a car is three times that of a bicycle. What are the speeds of cars and bicycles? (6 points)
29. It is known that △ABC is an equilateral triangle, d and f are points on the sides of BC and AB respectively, CD = BF, and AD is an equilateral △ ade.
① Q: Are△ △ACD and△ △CBF the same? Please explain the reason.
② When point D moves to where on BC line, the quadrilateral CDEF is a parallelogram, and ∠ DEF = 30? ? Try to prove your conclusion. (6 points)
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Examination time: 90 minutes. Proposition: Examination of the second grade preparation group: Zhang Tong Proofreading: Fei Guohua, Hu Chunlei.
Reference answer
I. 1, 2, 3, 7, 4, 5,
6, 8, 7, equal and equally divided 8, 2 9, isosceles right angle 10,
2. 1 1, C 12, A 13, C 14, C 15, a.
16、B 17、A 18、D 19、B 20、D
Iii. 2 1, 1023 180④
22、① ②
23.① Prove that the root increases and the original equation has no solution ②.
24. Proof: Yes, ‖ is the midpoint,,,,
,,, is a rectangle.
25. simplify it:
It doesn't matter when, when and the denominator.
When, when, the original form.
26. The square root of,, is.
27,,, primitive type
28. Solution: Let the bicycle speed be km/h and the car speed be km/h. ..
From the meaning of the question, then.
Answer: The bicycle speed is 12.5km/h, and the car speed is 37.5 km/h. ..
29、① 。
Prove that it is an equilateral triangle,,,,.
(2) When it is the midpoint, it satisfies the meaning of the question, it is the midpoint and an equilateral triangle, and bisecting,,, and is an equilateral triangle,,,,,
, , ,
Because.